Possible. The site mentioned by Mr. Hubbard states that recent dives indicate that the Phoenix was a sister ship to the Nashville. That site also mistakenly states that the Nashville was constructed at Montgomery. However, the O.R.'s clearly indicated that it was started at Selma by the same contractors [Porter and Watson] that were building the ironclads on the Tombigbee. Here's what I have on the two:

“Nashville” sidewheel ironclad ram. 1400 tons. [Construction started at Selma by Porter and Watson. Completed at the Mobile Yard in 1864. Burned in May, 1865 to prevent capture.]

"Phoenix" floating ironclad battery. [Construction completed at Mobile Yard in 1864. Burned to prevent capture in Jan. 1865.]

If the Phoenix was a sister ship to the Nashville, then it would stand to reason that it was also constructed by Porter and Watson.